Trapped Surface Formation for Spherically Symmetric Einstein–Maxwell-Charged Scalar Field System with Double Null Foliation

The formation of trapped surfaces in the gravitational collapse of spherically symmetric scalar fields with a positive cosmological constant

“…Later, in celebrated work [13], Christodoulou extended his criterion to the context of the Einstein vacuum equations without symmetry assumptions; in the mean time, important developments have been achieved in that setting [1-3, 29, 30]. Returning to the context of spherically symmetric spacetimes we would like to mention that criteria for the formation of trapped surfaces were also established for solutions of the Einstein-Vlasov equations, in [7], the Einstein-Euler system, in [9], and the Einstein-Maxwell-charged scalar field system, in [6]. Concerning the impact that the formation of a trapped surface has in the global structure of asymptotically flat spherically symmetric spacetimes we refer the reader to the qualitative results in [24,31] and the quantitative results obtained in [4,5,32].…”

Strong cosmic censorship in the presence of matter: the decisive effect of horizon oscillations on the black hole interior geometry

“…Having addressed the generic case in Conjecture 2, there remains still the possibility that there exist (nongeneric) Cauchy data for which the scalar field φ H + on the event horizon H + does not satisfy the (qualitative) oscillation condition (1-10). Indeed, on the basis of certain scattering arguments [Angelopoulos et al 2020;Masaood 2022] we conjecture. 4 Conjecture 3.…”

“…The EMKG model describes self-gravitating matter and provides a setting for studying spherical gravitational collapse of charged and massive matter if q 0 ̸ = 0 and m 2 ̸ = 0 (see the discussion in Section 1C3). This model has attracted much attention in the literature [An and Lim 2022;Bizoń and Wasserman 2000;Dias et al 2019;Kommemi 2013;Gajic and Luk 2019; 2021;; see also [Yang and Yu 2019;Lindblad and Sterbenz 2006;Klainerman and Machedon 1994;Krieger et al 2015;Rodnianski and Tao 2004] for work on the flat Minkowski background.…”

“…In view of this, for the blow-up statement of Theorem I (ii) these exceptional masses for which the scattering resonances are absent have to be excluded. Refer also to Häfner et al 2021] for a scattering theory of the Dirac equation on the interior of Reissner-Nordström and to [Bachelot 1994;Dimock and Kay 1987;Masaood 2022;Alford 2020] for scattering theories on the exterior.…”

“…There is yet another possible scenario in which the exteriors of AdS black holes are nonlinearly unstable (see [Moschidis 2017;2020;2023;Bizoń and Rostworowski 2011]) and the question of strong cosmic censorship would be thrown even more open.…”